We don’t need to know the values of \(t\); to find \(x\) and \(y\) it is sufficient to know \(\cos t\) and \(\sin t\). When \(\cos t=0\), \(\sin t = 1\) or \(-1\), so substituting we find the stationary points are at \[(0,3)\text{ and }(0,-3).\]

\(\dfrac{dy}{dx}\) is undefined when \(\sin t=0\) which happens at \[(-2,0) \text{ and } (2,0).\] A sketch of the curve should make it clear what is happening here.